orWatch a videoFind the correlation coefficient, r, of the data described below.Piquant Candy Company is testing a new additive designed to make its hard caramel candies dissolve more slowly. Company scientists gave several taste testers pieces of candy with varying amounts of the additive.The scientists recorded the amount of additive in each piece (in milligrams), x, and how long the taste tester said it took to dissolve completely (in minutes), y.Milligrams Minutes38 540 647 850 665 10Round your answer to the nearest thousandth.

Read the following description of a data set.Piquant Candy Company is testing a new additive designed to make its hard caramel candies dissolve more slowly. Company scientists gave several taste testers pieces of candy with varying amounts of the additive.The scientists recorded the amount of additive in each piece (in milligrams), x, and how long the taste tester said it took to dissolve completely (in minutes), y.The least squares regression line of this data set is:y=1.148x–92.855If a piece of candy has 92 milligrams of the additive, how long does the line predict it would take to dissolve completely?Round your answer to the nearest integer. minutes

Consider the data below:X1721161511242719Y7366617071906884Determine Pearson's product coefficient of correlation.Group of answer choices0.27480.0755-0.07850.9371

Deshawn wanted to find out how temperature affects the rate at which three packets of sugar dissolve in a liter of water.To find out, he performed a scientific investigation. The results from his investigation are shown below.Time (in seconds) for Sugar to Dissolve at Different TemperaturesTemperature Trial 1 Trial 2 Trial 3 Mean (average)25°C 123 s 127 s 124 s 125 s30°C 111 s 109 s 107 s 109 s35°C 98 s 101 s 97 s 99 sWhich of the following is true about the mean (average) values for the time it took the sugar to dissolve? A. The amount of time needed to dissolve the sugar stayed the same no matter what the temperature was. B. It is impossible to make any conclusions about Deshawn's experiment because he did not perform enough trials. C. The time needed for the sugar to dissolve decreased as the temperature increased. D. As the temperature increased, there was an increase in the amount of time needed to dissolve the sugar.

A team of researchers studying red wine were interested in using a linear model to predict the concentration of acetic acid based on the concentration of citric acid found in the wine.They randomly selected 106 bottles of red wine. Concentrations are measured in g/dm33. The amount of citric acid found in these wines ranged from 0.05 g/dm33 up to 1 g/dm33.Question 2.1 (1 mark)A correlation coefficient of -0.74 was calculated between the acetic and citric acids concentrations. Which ONE of the following plots is best described by this correlation coefficient?Plot DPlot BPlot CPlot AQuestion 2.2 (4 marks)They then used RStudio to construct a linear model to predict the acetic acid concentration in the red wine. Below is the summary output for this model.summary(wine.lm)## ## Call:## lm(formula = acetic.acid ~ citric.acid)## ## Residuals:## Min 1Q Median 3Q Max ## -0.16519 -0.06360 -0.02120 0.04675 0.29145 ## ## Coefficients:## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 0.49989 0.01800 27.77 <2e-16 ***## citric.acid -0.47058 0.04195 -11.22 <2e-16 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ## Residual standard error: 0.09254 on 104 degrees of freedom## Multiple R-squared: 0.5475, Adjusted R-squared: 0.5431 ## F-statistic: 125.8 on 1 and 104 DF, p-value: < 2.2e-16Use the drop-down menus and numerical answer boxes to complete the equation of this linear model. Round numbers to 3dp.Answer == Answer ++ Answer ×× AnswerQuestion 2.3 (1 mark)based on this linear model, which ONE of the following statements is correct?A red wine that has no citric acid is expected to have 0.5 g/dm33 of acetic acidA red wine that has 1 g/dm33 more citric acid than another is expected to have 0.5 g/dm33 more acetic acidA red wine that has no acetic acid is expected to have 0.5 g/dm33 of citric acidA red wine that has 1 g/dm33 more acetic acid than another is expected to have 0.471 g/dm33 less citric acidQuestion 2.4 (2 marks)One of the bottles of red wines had 0.08 g/dm33 of citric acid and 0.62 g/dm33 of tartaric acid.The value of the residual for this bottle of red wine is: Answer (round your answer to 3dp)Question 2.5 (4 marks)Is the normality condition satisfied?Based on the Answer, as we Answer observe Answer, we can say that the condition of normality is Answer.Question 2.6 (1 mark)What other conditions, in addition to normality, must be satisfied for the linear model to be valid?Choose ONE option.All expected counts are at least 5, representative, paired.Independence, equal spread and linearity.Paired, linearity and independence.Sample size at least 30, representative and linearity.Question 2.7 (3 marks)The test for the slope has a p-value of 1.2949329 × 10-19Decision: As the p-value is Answer than 0.05, we find in favour of the Answer.Conclusion:Choose ONE option.There is evidence that the slope is equal to -0.471There is evidence that the slope is not equal to 0.5There is evidence that the slope is not equal to 0There is evidence that the slope is equal to 0

A team of researchers studying red wine were interested in using a linear model to predict the concentration of acetic acid based on the concentration of citric acid found in the wine.They randomly selected 106 bottles of red wine. Concentrations are measured in g/dm33. The amount of citric acid found in these wines ranged from 0.05 g/dm33 up to 1 g/dm33.Question 2.1 (1 mark)A correlation coefficient of -0.74 was calculated between the acetic and citric acids concentrations. Which ONE of the following plots is best described by this correlation coefficient?Plot DPlot BPlot CPlot A